You’ve probably all seen a forest plot in a meta-analysis – it looks a bit like this:
I’m not going to explain a forest plot. This post is just about “weight”.
To calculate the contribution that each study should have on the position of the big diamond blob, each study is “weighted”.
How is it weighted you ask… well the weight of each study is calculated from the standard error of the relative risk in that study (on a log scale).
Larger trials usually have smaller standard errors, so they will usually carry more weight in the meta-analysis. This is not necessarily the case though – the number of events also influences the standard error (a large trial may still have a large standard error if the number of events was small).
To work out where the diamond blob should go, you simply smash out the below equation (basically a weighted mean):
The weights are often displayed as a percentage in the forest plot – this percentage is not used in the equations above.
The numerical equation for this weighted mean (combined effect size) is below if you really want it…
Σ= sum of…
Wi = individual study weight
Ti = individual study effect size
- A concice guide to clinical trials by Allan Hackshaw
- Handbook of parametric and nonparametric statistical procedures by David Sheskin